The ability to generalize from observed to new related environments is central to any form of reliable machine learning, yet most methods fail when moving beyond i.i.d data. This work argues that in some cases the reason lies in a misapreciation of the causal structure in data; and in particular due to the influence of unobserved confounders which void many of the invariances and principles of minimum error between environments presently used for the problem of domain generalization. This observation leads us to study generalization in the context of a broader class of interventions in an underlying causal model (including changes in observed, unobserved and target variable distributions) and to connect this causal intuition with an explicit distributionally robust optimization problem. From this analysis derives a new proposal for model learning with explicit generalization guarantees that is based on the partial equality of error derivatives with respect to model parameters. We demonstrate the empirical performance of our approach on healthcare data from different modalities, including image, speech and tabular data.
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